Visual Data Mining of Raster Data: A Volume

Visual Data Mining of Raster Data: A Volume-Rendering-Based Hierarchical Approach a

Fei Du *a, b, A-Xing Zhu a, c, Tao Pei a, Chengzhi Qin a State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, A 11, Datun Road, Anwai, Beijing 100101, China; b Graduate University of Chinese Academy of Sciences, 19 A, Yuquan Road, Beijing 100049, China; c Department of Geography, University of Wisconsin Madison, 550 North Park Street, Madison, WI 53706, USA.

ABSTRACT Developments of raster data capture technologies and demands from application fields call for advanced raster data analysis methods. Visual data mining that involves human’s visual analytical capability in data analysis attracts attention in recent years. Raster datasets usually have large amount of pixels, which may cause serious clotting problem in visualization and thus challenges visual data mining. The research reported here mainly focuses on this problem and tries to construct a hierarchical framework for visual data mining of raster data. In the hierarchical structure, the first level uses volume rendering to visualize the whole raster dataset in attribute space, which can greatly reduce the impact of clotting. To avoid the loss of subtle patterns, the second level makes use of parallel coordinates plot to reflect detailed attribute information. This hierarchical structure ensures that both global and local patterns embedded in data can be detected. In both levels, visualizations of attribute space are linked with that of geographic space. Software prototype was developed and then applied to find small clusters that may relate to possible soil types. Case study result demonstrated the effectiveness of this proposed approach. Keywords: visual data mining, raster data, large data size, clotting, attribute space, volume rendering, digital soil mapping

1. INTRODUCTION Data capture technologies of raster geo-spatial data have been advancing at a very fast pace over the past two decades. Aerial and space remote sensing sensors deliver considerable earth observation data everyday. At the same time, with the development of technology for creating more detailed digital elevation data, such as LIDAR1 and InSAR2, diverse regular grid DEM products have become increasingly available. Besides their availability, raster data are also characterized by their suitability for continuous surface modeling3, so they become more and more popular in geographic analysis. It has been recognized that capabilities of raster data mining have not kept up with the need for analyzing the increasingly large volumes of raster data that have been collected. Although there are various kinds of automatic algorithms for data mining tasks, the results are usually not reliable due to the complexity of geographical phenomenon and limitations of algorithms themselves. Visual data mining is considered to be a good complement to automatic algorithms. It involves human’s visual analytical capability in data analysis and emphasizes the integration of numeric data analysis techniques and the visual capability of human experts, so it provides the potential to increase reliability of the analysis result4. Similar to other types of geo-spatial data, raster data also consists of two pieces of information: spatial information (spatial location and spatial topology), which corresponds with geographic space, and attribute information which *

[email protected] International Conference on Earth Observation Data Processing and Analysis (ICEODPA), edited by Deren Li, Jianya Gong, Huayi Wu, Proc. of SPIE Vol. 7285, 72853W · © 2008 SPIE · CCC code: 0277-786X/08/$18 · doi: 10.1117/12.815718

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corresponds with attribute space. Both of them should be taken into consideration when designing visual data mining approaches and systems. Methods for visualizing raster data in geographic space are relatively mature. Unfortunately, visualization of raster data in attribute space encounters problems that are hard to be dealt with: Traditional visualization tools, such as scatter plots, which can be used to visualize vector data whose data size is relatively small in attribute space will face serious clotting problem when applied to large-volume raster dataset. That is, if every pixel (cell) is taken as a visualization unit in attribute space, the sheer volume of pixels in a large raster dataset will clot the display space of computer screen. Therefore, it’s difficult to visually discover important patterns, such as clusters and anomalies, embedded in the raster data. For example, two high-density classes and one low-density class can be visually detected from Fig. 1a, but when the data size becomes very large, as illustrated in Fig. 1b, it is quite hard to find any patterns by visualization. Low-Density Class

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From the above analysis, it is obvious that the challenge of visual data mining of raster data comes from the large data size and the corresponding clotting problem in attribute space visualization. So how to solve the clotting problem is one of the key points during realizing visual data mining of raster data. This research focuses on this issue and tries to provide a new visual data mining approach to support the discoveries of clusters and anomalies which are common tasks in raster data mining applications. The rest of this paper is organized as follows: Section 2 reviews existing solutions to visual data mining of raster data with focus on how they solve the clotting problem caused by large data size. In section 3, we propose a hierarchical approach that uses volume rendering5 to visualize whole raster dataset in attribute space (a global view) and applies parallel coordinates plot6 to visualize subset of interest in attribute space (a local view). In both these two levels, views for visualizing attribute space are linked with that of geographic space for the analysts to consider spatial information and attribute information simultaneously. Section 4 presents a software prototype of this approach. A case study in raster-based digital soil mapping is presented in Section 5. The last section summarizes this paper and discusses some directions for future research.

2. REVIEW OF EXISTING SOLUTIONS Visualizing raster data in geographic space has already been extensively studied and many well-developed methods, including image pyramid7 and 3D display8, have been proposed, so it will not be discussed in this paper. We focus our attention to the visualization of raster data in multi-dimensional attribute space which is vital to visual data mining. There are some studies on methods that are able to avoid clotting in visualization. A few of them can be or have already been used in visual data mining of raster data. Existing optional solutions fall into two types: spatial-centric approaches and attribute-centric approaches. 2.1

Spatial-centric approaches

Spatial-centric approaches take geographic space as the basic frame and try to visualize multi-dimensional attributes of each pixel on its spatial location.

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Traditionally, colors are used to represent attribute information. In remote sensing data analysis, three bands are selected and assigned red, green and blue colors, respectively, so the final images reflect three-dimensional attribute information in spatial location of each pixel. This can be regarded as a simple method of spatial-centric visualization of raster data. An improvement of this approach is Choropleth which is a classic technique in thematic cartography. When applying it in raster data visualization, pixels are classified according to their attribute values and every class is assigned a different color. Choropleth with interactive techniques can make it easier for analysts to locate particular values or expose initially unclear spatial patterns of raster data9. Another endeavor is to integrate multiple attributes into one. Image grand tour10 projects a linear combination of the multi-dimensional attributes into one-dimensional space and then renders these projected values as a gray-scale image. An animation of the projected images is generated by using different linear combinations. From the animation, analysts can visually detect multi-dimensional patterns. Some studies make efforts to replace pixels with icons or textures so that more attribute information is encoded. In iconbased techniques, every pixel is not represented by a single color but by an icon. The construction of icon takes several visual variables, such as color, length, width and shape, into consideration, so this method can carry more attributes than conventional pixel images11. A similar way is using texture to reflect multi-dimensional attributes in the frame of geographic space. Textures are generated by applying density, regularity, height, orientation, color of strips12. Spatial-centric approaches suffer little clotting problem. However, this kind of approaches is constrained by spatial location of pixels and the number of attributes which are displayed is limited. It would be difficult to visually analyze patterns in multi-dimensional attribute space. 2.2

Attribute-centric approaches

Attribute-centric approaches visualize data in attribute space directly. Visualization of attribute space can be linked with that of geographic space if necessary. Free to the constraints of spatial locations, these approaches are more flexible. Currently, two ways for attribute-centric approaches are adopted: improving graphics and reducing data size. 2.2.1

Improving graphics

Many studies focus on how to improve graphic to support large dataset. There are mainly two endeavors: (1) Adding transparency For methods of this kind, every pixel is still treated as a visualization unit in attribute space, but they are not opaque and instead, transparency is added to visualization units (polylines, points, etc.) so that units “behind” them can be seen13. These methods do have some effects. However, when it comes to raster datasets, since the data size is usually so large that even adding transparency cannot reveal data patterns clearly. (2) Rearranging visualization units Another idea is to rearrange visualization units to maximize the amount of information represented at one time without overlap. A typical method is pixel-oriented visualization14. Its basic idea is to represent each attribute value as a single colored pixel, mapping the range of possible attribute values to a fixed color map and displaying different attributes in different sub-windows. This kind of methods makes full use of computer screen space, but since a dimension of one pixel of raster data takes up one screen pixel, large data size and multi-dimensionality of raster dataset may easily exceed the capability of the screen display. 2.2.2

Reducing data size

It’s usually difficult to visualize the whole raster dataset, therefore, a solution easy to think of is to reduce the size of datasets to a “controllable” level, and then visualize them. Three approaches are frequently used: (1) Using statistical method Statistical methods are able to reduce data size by summarizing data as statistics. For large raster dataset, one does not need to visualize every pixel in attribute space, and instead, one can transfer the dataset to some statistics, such as maximum value, minimum value, and mean value. Then statistical graphic tools, for example, box plot and stem-leaf plot, could be used to visualize these aggregation results. These methods have already been used in remote sensing image analysis15, 16. Generally, they have good scaling-up capabilities. However, they only reflect statistical information and

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detailed information is dropped. Besides, most tools only take one-dimensional attribute, so patterns in multidimensional attribute space are ignored. (2) Selecting part of data A common technique of selecting data is sampling. It can be done in geographic space or attribute space. Systematic and random sampling has been applied to remote sensing image and the selected pixels are visualized by scatter plots17, 18. Besides sampling, another strategy is to cut a portion of data for visualization. A typical case is spatial spectrogram19 which cuts part of a hyperspectral image and visualizes them using 2D graph. The effectiveness of this kind of methods is largely affected by how to select data. Most of the time, the loss of subtle information in original dataset is unavoidable. (3) Coarsening data Many methods can be used to coarsen data before visualization, such as filtering, clustering, etc. Take clustering as an example, after this operation, the original dataset are represented by cluster centers, so the data size is greatly decreased. Some studies have applied hierarchical cluster algorithms to large dataset and improved parallel coordinates plot to visualize the cluster result20. Coarsening data may help analyst to seize main patterns quickly. However, the subjectivity of choosing coarsening algorithms (e.g. cluster algorithms) may lead problems. It is possible that we “force” data appear as what are expected when applying algorithms. Another problem is also the loss of subtle patterns.

3. A VOLUME-RENDERING-BASED HIERARCHICAL APPROACH Existing solutions cannot effectively visualize large raster datasets and some important patterns may be lost during the data preparation or at the time of visualization. Besides, most of them are not designed specifically for visual data mining of raster data and thus cannot support raster data analysis tasks well. In order to overcome the defects and realize visual data mining of raster data, new framework should be designed and implemented. There are many ideas that could be borrowed from exiting methods, such as adding transparency, coarsening data, selecting part of data, and so on. The advancement of computer graphics, especially 3D techniques, provides new possibilities for data visualization. Based on these, we propose a hierarchical approach guided by Information Seeking Mantra that is “overview first, zoom and filter, and then details-on-demand”21. This hierarchical approach consists of two levels: The first level is global visualization which uses binning to preprocess raster dataset and then uses volume rendering to visualize the entire raster dataset in attribute space. The second level makes use of a well-known visualization tool, parallel coordinates plot, to visualize part of raster dataset in attribute space. In both levels, views for visualizing attribute space are linked with that of geographic space. Fig. 2 shows the basic framework of the new approach.

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3.1

Level 1: visualizing the whole dataset using volume rendering

The term volume rendering is used to describe techniques which allow the visualization of three-dimensional data. It is a rapidly growing field in both computer graphics and data visualization. These techniques are prevalent in medicine, astrophysics, chemistry, mechanical engineering, etc. In recent years, many volume rendering methods which can only run on workstations before can be implemented in personal computers. This greatly enlarges its application range. A three-dimensional array of elements is referred to as a volume and an element is refereed to as a voxel. A volume may be visualized by extracting surfaces of equal values from the volume and rendering them as polygonal meshes or by rendering the volume directly as a block of data. In this research, volume rendering refers to the latter one, that is direct volume rendering. Voxels are the basic units of a volume (Fig. 3). A voxel has a location in three-dimensional space and it is represented by opacity and color.

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Fig. 3. Voxels in a volume

For raster dataset, analysts choose three attributes of interest from multiple attributes to construct the three-dimensional attribute space. Then a voxel can be used to represent several pixels that are within certain range in this threedimensional attributes space. Such mapping from pixels to voxels is finished by binning operation: The threedimensional attribute space is divided into m×n×k small cubes (m, n, k are integers) and each cube is corresponding to a voxel; the number of pixels that fall into each cube is computed, so we get the density information of each voxel. After finishing this operation, the data size of the raster dataset is greatly reduced. Meanwhile, data patterns, especially density information, are preserved. The density information that associates with each voxel is encoded into opacity and color. This is controlled by transfer function. Transfer function can be a simple ramp, a piecewise linear function or an arbitrary table. Because every voxel has opacity value (transparency), the “inside” of the whole three-dimensional attribute space can be seen from outside by analysts. Hence, the clotting problem that is caused by large data size of raster data is solved. . It must be mentioned that when the volume data (binned data) are prepared, an appropriate direct volume rendering techniques should be chosen to visualize them. This will decide how the opacity and color are projected on frame buffer of the computers. There are many volume rendering techniques, including ray casting5, Splatting22, Shear Warp23, 24, texture mapping25, etc. Different methods have different rendering speeds and effects. For visual data mining application, since analysts may interact with the visualization frequently, response speed should be given high priority when choosing volume rendering technique. In final volume-rendering-based view, data density distribution in three-dimensional attribute space is clearly expressed by different opacity and color. Analysts can rotate, zoom in, and zoom out to detect patterns that they are interested in. Besides, they can also adjust transfer function dynamically to change the mapping from density to opacity and color to highlight some interesting patterns.

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3.2

Level 2: visualizing partial dataset using parallel coordinates plot

Volume rendering provides an opportunity to efficaciously visualize the whole raster dataset in attribute space because the data size is reduced while the density information of data is well reserved. However, some “small” patterns may be lost during binning operation. A good visual data mining solution should support the discovery of both global (coarse) and local (detailed) patterns. When exploring in the volume-rendering-based global view, analysts could select part of the data for further analysis. Selection is conducted in three-dimensional attribute space. When a few voxels are selected, pixels which are within these voxels are extracted. At this time, the amount of pixels is greatly reduced, so every pixel can be taken as a visualization unit and binning process is not needed any more. Therefore, many traditional Information Visualization methods could be directly applied. Since the aim of this level is to see the detail, we should make the loss of information as small as possible, so those visualization tools that can reflect multi-dimensional patterns are more suitable. Parallel coordinates plot is a representative technique to visualize multi-dimensional data. It can visualize a high-dimensional dataset in a view without losing data and dimension. Although it may face the clotting problem during visualizing largevolume dataset, it can provide a good multi-dimensional visualization tool to analysis the interest sub-dataset which analysts select in the volume-rendering-based global attribute space view. In this local visualization view, interaction tools, such as selection tools, are also important in assisting analysts to explore the data. 3.3

Linking attribute space visualization with geographic space visualization

Visual data mining of raster geo-spatial data is different from that of non-spatial data because spatial information should be taken into account. Attribute space visualization only reflects attribute information. Only linking it with geographic space visualization can some patterns with true geographic meanings become clear and easy to be detected. There are two options for visualizing geographic space: two-dimensional display or three-dimensional display. For twodimensional representations, it’s easy for the analysts to interact, and it gives plan metric view thus provides good sense of position. For three-dimensional representation, it gives a stereo metric view of the distribution of attribute value across space, so it provides good sense of reality. In both 2D and 3D views, RGB color composition (assigning three attributes red, green and blue color) can be used to display raster data. Both the global and local attribute space visualization views are linked with geographic space visualization view. From the volume-rendering-based global view, analysts can use selection tools to locate interesting patterns by rotating, zooming in/out or adjusting transfer functions. In local view, analysts can also select data of concern. When the selection is done, the linked geographic space view will change accordingly, that is, the corresponding pixels will be highlighted in geographic view. Such linking help analysts visually explore patterns in attribute space and geographic space simultaneously.

4. PROTOTYPE SYSTEM The volume-rendering-based hierarchical approach for visual data mining of raster data presented above has been implemented in a software prototype. The system is developed mainly with Java programming language and Visualization Toolkit (VTK). Java is a well-known platform-free programming language and has already been widely applied. Particularly, there are a lot of powerful Java packages that can be used to construct complicated applications quickly. VTK is an open source, freely available software package for 3D computer graphics and visualization adopted by thousands of researchers and developers around the world. VTK consists of a C++ class library, and several interpreted interface layers, such as Java Tcl/Tk, and Python. VTK supports a wide variety of visualization algorithms including volume rendering methods. This can greatly facilitate the development of visualization systems. In this prototype system, VTK is mainly used to realize volume-rendering-based attribute space visualization. Both Java and VTK are platform independent, so the prototype system can be easily transport to other platform. The prototype system could take different raster data formats as input, such as GeoTIFF, ERDAS Imagine Images. When the dataset is read in, analysts choose three attributes to construct three dimensions of volume data. Then the whole

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dataset can be visualized by volume rendering. In the prototype system, we choose 2D Texture Mapping as the direct volume rendering technique. Compared with other techniques, 2D Texture Mapping has fast rendering speed, so it can satisfy the need of real-time interaction. The effect of volume rendering in attribute space is shown in Fig. 4. Different opacities and colors (in printed paper, colors are converted to grayscales) represent density distribution of pixels in attribute space. Ginbal Vinnn1 Tool i

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Analysts could also make use of selection tools (box) to lock part of the data (Fig. 6a) and highlight the corresponding pixels in geographic space visualization view to see their spatial distribution (Fig. 6b). The selected pixels are represented with yellow color here (in printed paper, colors are converted to grayscales). C.ogr.phi

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When part of the data is selected in volume-rendering-based global view, they can also be exported to local visualization view to get more detailed information (Fig. 7). Local Visual TooJ in 4ttribute Sice:. P mild Coordinate, Plot

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5. AN APPLICATION The new approach has been applied in digital soil mapping to test its efficiency. Digital soil mapping is the computerassisted production of digital maps of soil type and soil properties26. It uses mathematical and statistical models to predict variations of soil types or properties over space by using existing environmental data. The commonly used environmental data in digital soil mapping are remote sensing data and terrain data (DEM and other terrain attributes derived from DEM).

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According to soil-landscape model theory, spatial distribution of soil types are largely decided by environmental factors, such as terrain, climate, geology, etc. So if we applying clustering operation on environmental data, the clusters can represents soil types to a great extent27. Current cluster algorithms tend only to find large clusters while small clusters are omitted. In fact, some soil types may occur within very small regions, so small clusters are also of importance. Visual data mining can be used to help analysts find small clusters that may represent possible soil types. However, because of clotting problem caused by large data size of raster environmental dataset, existing solutions have limited capability to support this need. Our software prototype has been used to carry out this task. The study area locates in Heshan farm Nenjiang county Heilongjiang province in China. Regular grid DEM data with 10m grid size and other terrain attributes data were used to construct multi-dimensional raster dataset because terrain is thought to be the decisive factor of the spatial variations of soil types in the study area28. The size of the raster dataset is 1113×932. Fig. 8 displays the seven chosen attributes. They are: elevation, aspect, slope, planform curvature, profile curvature, wetness index and relative position index.

Fig. 8. DEM and terrain attributes used in the case study (from left to right): elevation, aspect, slope, planform curvature, profile curvature, wetness index and relative position index

Firstly, we chose three attributes from the raster terrain dataset. With “Density to Opacity & Color” editor in the software prototype, we can set the opacity value of high-density voxels to be zero, so only the low-density voxel were displayed with color in volume-rendering-based attribute space view. Some of those low-density voxels that have geographic meanings were then selected with selection tool. For example, in Fig. 9a, those voxels represent areas with high slope and low wetness index were locked. In these areas, water condition is poor, so it’s quite possible that a soil type may appear here. The corresponding pixels in geographic space were displayed with highlighted yellow color, as is shown in Fig. 9b (in printed paper, colors are converted to grayscales). The selected pixels can also be exported to local visualization tools to be visually analyzed in detail. This visual exploration process could be iterative. Aided by domain knowledge, some low-density clusters (both in attribute space and geographic space) which indicate possible soil type locations were extracted. It proves to be a good supplement to automatic clustering algorithms. Rd

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Fig. 9. Detection of small clusters that may represent soil types

The case study demonstrated the following positive effects of our visual data mining approach and the prototype system: The first one is the opportunity for understanding the multi-dimensional raster dataset, especially its unique patterns in

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attribute space and geographic space; The other one is the enhanced ability to produce hypotheses and discover patterns based on visual perception and domain knowledge, such as the discovery of low-density clusters which indicate potential soil type locations in this case study.

6. CONCLUSIONS AND FUTURE WORKS Raster data become increasingly important in geo-spatial sciences and applications. Visual data mining is thought of as an efficacious way to involve human’s visual analytical ability into data analysis, so it has broad prospects. The large data size of raster dataset results in clotting problem during visualization and thus makes visual data mining of raster data a challenging issue. In this paper, we firstly reviewed existing solutions. Based on them and the development of computer graphics, we proposed a volume-rendering-based hierarchical approach and meanwhile implemented a prototype system. Hierarchical structure makes both the overall and subtle patterns be visually detected. In the global level, volume rendering can effectively visualize the whole raster dataset in attribute space and suffers little problem of clotting. In the local level, parallel coordinates plot can preserve multi-dimensional attribute information. Besides, the linking between attribute space visualization with geographic space visualization distinguishes visual data mining of raster data with that of other types of data and it facilitates discovering valuable patterns of geographic meanings. The application in digital soil mapping proved that it has considerable appeal in assisting analysts visually explore raster data and find useful patterns. Nevertheless, the proposed approach needs to be improved in some aspects. Currently, opacity and color are all used to express density information. In fact, color can also encode attribute information. If so, volume rendering could visualize more dimensions. In addition, current approach only links attribute space with geographic space. A better way is realizing double linking, that is, selected data in attribute space will be highlighted in geographic space and vice versa. However, since the volume-rendering-based attribute space visualization uses voxels to represent data, how to handle the non-correspondence of pixels and voxels is the key point in double linking. In the future, besides improving the approach itself, we plan to integrate computational methods (such as clustering algorithms) with visualization. Current method mainly focuses on visualization, in fact, for raster data analysis, automatic algorithms are also very important, so a better combination of visual and computational approaches will greatly enhance data analysis capability. In addition, we plan to collect feedback from domain experts to modify our approach and make it support the needs of various application fields.

ACKNOWLEDGEMENTS This study is supported by National Basic Research Program of China (No. 2007CB407207); Chinese Academy of Sciences International Partnership Project "Human Activities and Ecosystem Changes" (No. CXTD-Z2005-1); National Key Basic Research Program of China (No. 2006CB701305) and National Natural Science Foundation of China (No. 40501056).

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